It is known to prepare compounds of formula I by reacting the corresponding alcohols of formula R.sub.n --OH, wherein R.sub.n typically has the meanings given for R in the definition of formula I, with formaldehyde or paraformaldehyde in the presence of an aqueous acid, e.g. of the corresponding hydrohalic acid (HBr or HCl) (q.v. Olah, G. A., et al., "Haloalkylations", in: Friedel-Crafts and Related Reactions, Vol. II, J. Wiley & Sons, New York, 1964, pp. 659-671 and 734-737; and U.S. Pat. No. 4,568,700, published Feb. 4, 1986). The drawback of the known processes is that (especially if R in R.sub.n --OH is a secondary hydrocarbon radical, but also if R is a primary hydrocarbon radical) a substantial number of largely unwanted by-products are formed which result in a loss of yield, including also in particular the carcinogenic, and hence chronically toxic, bis(1-halo-lower alk-1-yl) ethers, for example the bis(chloromethyl) ether (cf. Tou., J. C., et at., "Possible Formation of bis(chloromethyl) ether from the Reactions of Formaldehyde and Chloride Ion", Anal. Chem. 48(7), 958-63 (1976)), and/or hinder working up.